# Compound of six square antiprisms

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Compound of six square antiprisms
Rank3
TypeUniform
Notation
Bowers style acronymGidsac
Elements
Components6 square antiprisms
Faces48 triangles, 12 squares as 6 stellated octagons
Edges48+48
Vertices48
Vertex figureIsosceles trapezoid, edge length 1, 1, 1, 2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {4+{\sqrt {2}}}{8}}}\approx 0.82267}$
Volume${\displaystyle 2{\sqrt {4+3{\sqrt {2}}}}\approx 5.74200}$
Dihedral angles3–3: ${\displaystyle \arccos \left({\frac {1-2{\sqrt {2}}}{3}}\right)\approx 127.55160^{\circ }}$
4–3: ${\displaystyle \arccos \left({\frac {{\sqrt {3}}-{\sqrt {6}}}{3}}\right)\approx 103.83616^{\circ }}$
Central density6
Number of external pieces336
Level of complexity52
Related polytopes
ArmySemi-uniform Girco, edge lengths ${\displaystyle {\sqrt {\frac {2-{\sqrt {2}}}{2}}}}$ (ditetragon-rectangle), ${\displaystyle {\frac {{\sqrt[{4}]{2}}-{\sqrt {2-{\sqrt {2}}}}}{2}}}$ (ditetragon-ditrigon), ${\displaystyle {\frac {{\sqrt[{4}]{2}}-{\sqrt {2+{\sqrt {2}}}}}{2}}}$ (ditrigon-rectangle)
RegimentGidsac
DualCompound of six square antitegums
ConjugateCompound of six square antiprisms
Abstract & topological properties
Flag count384
OrientableYes
Properties
SymmetryB3, order 48
Flag orbits8
ConvexNo
NatureTame

The great disnub cube, gidsac, or compound of six square antiprisms is a uniform polyhedron compound. It consists of 48 triangles and 12 squares (which pair up into 6 stellated octagons due to lying in the same plane), with one square and three triangles joining at a vertex.

It can be formed by combining the two chiral forms of the great snub cube.

Its quotient prismatic equivalent is the square antiprismatic hexateroorthowedge, which is eight-dimensional.

## Vertex coordinates

The vertices of a great disnub cube of edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\sqrt {\frac {2+{\sqrt {2}}}{8}}},\,\pm {\sqrt {\frac {2-{\sqrt {2}}}{8}}},\,\pm {\frac {\sqrt[{4}]{8}}{4}}\right)}$.